22,074 research outputs found
Bose-Einstein condensation in complex networks
The evolution of many complex systems, including the world wide web, business
and citation networks is encoded in the dynamic web describing the interactions
between the system's constituents. Despite their irreversible and
non-equilibrium nature these networks follow Bose statistics and can undergo
Bose-Einstein condensation. Addressing the dynamical properties of these
non-equilibrium systems within the framework of equilibrium quantum gases
predicts that the 'first-mover-advantage', 'fit-get-rich' and
'winner-takes-all' phenomena observed in competitive systems are
thermodynamically distinct phases of the underlying evolving networks
Topology of evolving networks: local events and universality
Networks grow and evolve by local events, such as the addition of new nodes
and links, or rewiring of links from one node to another. We show that
depending on the frequency of these processes two topologically different
networks can emerge, the connectivity distribution following either a
generalized power-law or an exponential. We propose a continuum theory that
predicts these two regimes as well as the scaling function and the exponents,
in good agreement with the numerical results. Finally, we use the obtained
predictions to fit the connectivity distribution of the network describing the
professional links between movie actors.Comment: 13 pages, 3 figure
Giant strongly connected component of directed networks
We describe how to calculate the sizes of all giant connected components of a
directed graph, including the {\em strongly} connected one. Just to the class
of directed networks, in particular, belongs the World Wide Web. The results
are obtained for graphs with statistically uncorrelated vertices and an
arbitrary joint in,out-degree distribution . We show that if
does not factorize, the relative size of the giant strongly
connected component deviates from the product of the relative sizes of the
giant in- and out-components. The calculations of the relative sizes of all the
giant components are demonstrated using the simplest examples. We explain that
the giant strongly connected component may be less resilient to random damage
than the giant weakly connected one.Comment: 4 pages revtex, 4 figure
A Geometrical Test of the Cosmological Energy Contents Using the Lyman-alpha Forest
In this Letter we explore a version of the test of cosmological geometry
proposed by Alcock and Paczynski (1979), using observations of the Lyman-alpha
forest in the spectra of close quasar pairs. By comparing the correlations in
absorption in one quasar spectrum with correlations between the spectra of
neighboring quasars one can determine the relation of the redshift distance
scale to the angle distance scale at the redshift of the absorbers, . Since this relationship depends on the parameters of the cosmological
model, these parameters may be determined using the Lyman-alpha forest. While
this test is relatively insensitive to the density parameter in a
dust-dominated universe, it is more sensitive to the presence of a matter
component with large negative pressure (such as a cosmological constant
) and its equation of state. With only 25 pairs of quasar spectra at
angular separations , one can discriminate between an open universe () and an flat
(-dominated) universe at the level. The S/N can be enhanced
by considering quasar pairs at smaller angular separations, but requires proper
modeling of nonlinear redshift space distortions. Here the correlations and
redshift space distortions are modeled using linear theory.Comment: 13 pages, 2 ps figures, submitted to ApJ
Effect of the accelerating growth of communications networks on their structure
Motivated by data on the evolution of the Internet and World Wide Web we
consider scenarios of self-organization of the nonlinearly growing networks
into free-scale structures. We find that the accelerating growth of the
networks establishes their structure. For the growing networks with
preferential linking and increasing density of links, two scenarios are
possible. In one of them, the value of the exponent of the
connectivity distribution is between 3/2 and 2. In the other, and
the distribution is necessarily non-stationary.Comment: 4 pages revtex, 3 figure
Scaling properties of scale-free evolving networks: Continuous approach
Scaling behavior of scale-free evolving networks arising in communications,
citations, collaborations, etc. areas is studied. We derive universal scaling
relations describing properties of such networks and indicate limits of their
validity. We show that main properties of scale-free evolving networks may be
described in frames of a simple continuous approach. The simplest models of
networks, which growth is determined by a mechanism of preferential linking,
are used. We consider different forms of this preference and demonstrate that
the range of types of preference linking producing scale-free networks is wide.
We obtain also scaling relations for networks with nonlinear, accelerating
growth and describe temporal evolution of arising distributions. Size-effects -
cut-offs of these distributions - implement restrictions for observation of
power-law dependences. The main characteristic of interest is so-called degree
distribution, i.e., distribution of a number of connections of nodes. A scaling
form of the distribution of links between pairs of individual nodes for the
growing network of citations is also studied. We describe effects that produce
difference of nodes. ``Aging'' of nodes changes exponents of distributions.
Appearence of a single ``strong'' node changes dramatically the degree
distribution of a network. If its strength exceeds some threshold value, the
strong node captures a finite part of all links of a network. We show that
permanent random damage of a growing scale-free network - permanent deleting of
some links - change radically values of the scaling exponents. We describe the
arising rich phase diagram. Results of other types of permanent damage are
described.Comment: 21 pages revtex (twocolumn), 9 figure
Preferencial growth: exact solution of the time dependent distributions
We consider a preferential growth model where particles are added one by one
to the system consisting of clusters of particles. A new particle can either
form a new cluster (with probability q) or join an already existing cluster
with a probability proportional to the size thereof. We calculate exactly the
probability \Pm_i(k,t) that the size of the i-th cluster at time t is k. We
analyze the asymptotics, the scaling properties of the size distribution and of
the mean size as well as the relation of our system to recent network models.Comment: 8 pages, 4 figure
Weighted Evolving Networks
Many biological, ecological and economic systems are best described by
weighted networks, as the nodes interact with each other with varying strength.
However, most network models studied so far are binary, the link strength being
either 0 or 1. In this paper we introduce and investigate the scaling
properties of a class of models which assign weights to the links as the
network evolves. The combined numerical and analytical approach indicates that
asymptotically the total weight distribution converges to the scaling behavior
of the connectivity distribution, but this convergence is hampered by strong
logarithmic corrections.Comment: 5 pages, 3 figure
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